A conventional arrangement of a current driver comprises a current source for providing a supply current, and a current mirror. The supply current is supplied to the input circuit of the current mirror. At the output of the current mirror, a current with an adjusted current mirror ratio relative to the supply current is provided. The switch-on behavior is influenced by parasitic effects such as parasitic capacitances, which can additionally vary due to the manufacturing process, as well as temperature and voltage dependence. In the field of such current drivers in which current mirrors are used to achieve a defined switch-on behavior, long and variable switch-on times consequently represent a problem. This problem is particularly severe for current drivers that are used in high-frequency circuits such as LED controllers. For example, a high-resolution pulse width modulation on which this application is based places special requirements on the transition behavior when a current driver is switched on.